Just pulling your reports should not. However, some CAs do soft or hard pulls periodically, even if the SOL has expired.
If you've applied with ABC Mortgage Company, XYZ Mortgage Company, and PDQ Mortgage Company, then a CA might figure out that you're house hunting and it's time to try again.
Just pulling reports should not be a problem. But it sounds like you're more interesting in some credit rehab, and that isn't really a strong point of this forum. Knowing the SOL on debts will help a lot.
creditinfocenter is where I go. PM me if you want a few helpful starting points over there.